Methods and systems to facilitate reducing cone beam artifacts in images

ABSTRACT

Methods and systems for generating images from a set of projection data acquired during a CT scan is provided. The system includes a computer programmed to utilize at least one of a cone angle dependent view weighting and an image plane dependent view weighting to generate an image.

BACKGROUND OF THE INVENTION

This invention relates generally to computed tomography (CT) imaging andmore particularly, to reducing cone beam artifacts in CT images.

The original Feldkamp, Davis, and Kress (FDK) algorithm for a circulartrajectory has been extensively employed in medical and industrialimaging applications. With increasing cone angle, cone beam (CB)artifacts associated with the FDK algorithm deteriorate, because acircular trajectory does not satisfy the so-called data sufficiencycondition (DSC). A few “circular plus” trajectories, such as“circle+circle”, “ellipse+ellipse”, “circle+line”, “circle+arc”, havebeen proposed to facilitate reducing CB artifacts by meeting the DSC.However, the circular trajectory possesses advantages in medicalimaging, such as perfusion, cardiac and vascular imaging, as well asbreast and head imaging applications.

BRIEF DESCRIPTION OF THE INVENTION

In one embodiment, a computer programmed to generate computedtomographic (CT) images from a set of projection data acquired during aCT scan is provided. The computer is programmed to perform at least oneof a cone angle dependent view weighting and an image plane dependentview weighting.

In another embodiment, a method for producing a cross-sectional image ofan object by using a computed tomography imaging system is provided. Thesystem includes a source of a conical beam of radiation and a multi-rowdetector array arranged on opposite sides of an axis of rotation. Themethod includes rotating the source and detector array about the axis ofrotation, and while rotating, collecting x-ray attenuation data samplesfrom the multi-row detector array at a plurality of projection angles toproduce a set of projection data measured with a circular orbit of thex-ray source. The method further includes applying afiltered-backprojection algorithm to the set of projection data. Thealgorithm includes at least one of a cone angle dependent view weightingand an image plane dependent view weighting.

In yet another embodiment, a computed tomographic (CT) imaging systemfor reconstructing an image of an object is provided. The imaging systemincludes a detector array, at least one radiation source, and a computercoupled to the detector array and the radiation source. The computer isconfigured to apply a cone-angle-and-image-plane-dependent viewweighting function to a filtered backprojection algorithm to reconstructthree dimensional images from cone-beam projections measured with acircular orbit of the radiation source, and generate images using theview weighted filtered backprojection algorithm.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 is a pictorial view of a multi slice volumetric CT imagingsystem;

FIG. 2 is a block schematic diagram of the multi slice volumetric CTimaging system illustrated in FIG. 1;

FIG. 3 is a schematic illustration of an exemplary cone beam (CB)geometry that may be used with the imaging system shown in FIG. 1;

FIG. 4 is a schematic illustration of an exemplary cone-parallelgeometry, which can be obtained by a row-wise fan-to-parallel rebinningin the original CB geometry shown in FIG. 3;

FIG. 5 is a schematic diagram of an exemplary geometry of a direct-rayand its conjugate ray; and

FIG. 6 is a schematic diagram of an exemplary geometry of direct-raysand conjugate rays associated with a dual circular trajectory.

DETAILED DESCRIPTION OF THE INVENTION

In some known CT imaging system configurations, a radiation sourceprojects a fan-shaped beam which is collimated to lie within an X-Yplane of a Cartesian coordinate system and generally referred to as an“imaging plane”. The radiation beam passes through an object beingimaged, such as a patient. The beam, after being attenuated by theobject, impinges upon an array of radiation detectors. The intensity ofthe attenuated radiation beam received at the detector array isdependent upon the attenuation of a radiation beam by the object. Eachdetector element of the array produces a separate electrical signal thatis a measurement of the beam attenuation at the detector location. Theattenuation measurements from all the detectors are acquired separatelyto produce a transmission profile.

In third generation CT systems, the radiation source and the detectorarray are rotated with a gantry within the imaging plane and around theobject to be imaged such that an angle at which the radiation beamintersects the object constantly changes. A group of radiationattenuation measurements, i.e., projection data, from the detector arrayat one gantry angle is referred to as a “view”. A “scan” of the objectincludes a set of views made at different gantry angles, or view angles,during one revolution of the radiation source and detector.

In an axial scan, the projection data is processed to reconstruct animage that corresponds to a two dimensional slice taken through theobject. One method for reconstructing an image from a set of projectiondata is referred to in the art as the filtered back projectiontechnique. This process converts the attenuation measurements from ascan into integers called “CT numbers” or “Hounsfield units”, which areused to control the brightness of a corresponding pixel on a displaydevice.

To reduce the total scan time, a “helical” scan may be performed. Toperform a “helical” scan, the patient is moved while the data for theprescribed number of slices is acquired. Such a system generates asingle helix from a fan beam helical scan. The helix mapped out by thefan beam yields projection data from which images in each prescribedslice may be reconstructed.

As used herein, an element or step recited in the singular and precededwith the word “a” or “an” should be understood as not excluding pluralsaid elements or steps, unless such exclusion is explicitly recited.Furthermore, references to “one embodiment” of the present invention arenot intended to be interpreted as excluding the existence of additionalembodiments that also incorporate the recited features.

Also as used herein, the phrase “reconstructing an image” is notintended to exclude embodiments of the present invention in which datarepresenting an image is generated but a viewable image is not.Therefore, as used herein the term, “image,” broadly refers to bothviewable images and data representing a viewable image. However, manyembodiments generate (or are configured to generate) at least oneviewable image. Additionally, although described in detail in a CTmedical setting, it is contemplated that the benefits accrue to allimaging modalities including, for example, ultrasound, MagneticResonance Imaging, (MRI), Electron Beam CT (EBCT), Positron EmissionTomography (PET), Single Photon Emission Computed Tomography (SPECT),and in both medical settings and non-medical settings such as anindustrial setting or a transportation setting, such as, for example,but not limited to, a baggage scanning CT system for an airport or othertransportation center.

FIG. 1 is a pictorial view of a CT imaging system 10. FIG. 2 is a blockschematic diagram of system 10 illustrated in FIG. 1. In the exemplaryembodiment, a computed tomography (CT) imaging system 10, is shown asincluding a gantry 12 representative of a “third generation” CT imagingsystem. Gantry 12 has a radiation source 14 that projects a cone beam 16of X-rays toward a detector array 18 on the opposite side of gantry 12.

Detector array 18 is formed by a plurality of detector rows (not shown)including a plurality of detector elements 20 which together sense theprojected X-ray beams that pass through an object, such as a medicalpatient 22. Each detector element 20 produces an electrical signal thatrepresents the intensity of an impinging radiation beam and hence theattenuation of the beam as it passes through object or patient 22. Animaging system 10 having a multislice detector 18 is capable ofproviding a plurality of images representative of a volume of object 22.Each image of the plurality of images corresponds to a separate “slice”of the volume. The “thickness” or aperture of the slice is dependentupon the thickness of the detector rows.

During a scan to acquire radiation projection data, gantry 12 and thecomponents mounted thereon rotate about a center of rotation 24. FIG. 2shows only a single row of detector elements 20 (i.e., a detector row).However, multislice detector array 18 includes a plurality of paralleldetector rows of detector elements 20 such that projection datacorresponding to a plurality of quasi-parallel or parallel slices can beacquired simultaneously during a scan.

Rotation of gantry 12 and the operation of radiation source 14 aregoverned by a control mechanism 26 of CT system 10. Control mechanism 26includes a radiation controller 28 that provides power and timingsignals to radiation source 14 and a gantry motor controller 30 thatcontrols the rotational speed and position of gantry 12. A dataacquisition system (DAS) 32 in control mechanism 26 samples analog datafrom detector elements 20 and converts the data to digital signals forsubsequent processing. An image reconstructor 34 receives sampled anddigitized radiation data from DAS 32 and performs high-speed imagereconstruction. The reconstructed image is applied as an input to acomputer 36 which stores the image in a mass storage device 38.

Computer 36 also receives commands and scanning parameters from anoperator via console 40 that has a keyboard. An associated cathode raytube display 42 allows the operator to observe the reconstructed imageand other data from computer 36. The operator supplied commands andparameters are used by computer 36 to provide control signals andinformation to DAS 32, radiation controller 28 and gantry motorcontroller 30. In addition, computer 36 operates a table motorcontroller 44 which controls a motorized table 46 to position patient 22in gantry 12. Particularly, table 46 moves portions of patient 22through gantry opening 48.

In one embodiment, computer 36 includes a device 50, for example, afloppy disk drive or CD-ROM drive, for reading instructions and/or datafrom a computer-readable medium 52, such as a floppy disk or CD-ROM. Inanother embodiment, computer 36 executes instructions stored in firmware(not shown). Generally, a processor in at least one of DAS 32,reconstructor 34, and computer 36 shown in FIG. 2 is programmed toexecute the processes described below. Of course, the method is notlimited to practice in CT system 10 and can be utilized in connectionwith many other types and variations of imaging systems. In oneembodiment, Computer 36 is programmed to perform functions describedherein, accordingly, as used herein, the term computer is not limited tojust those integrated circuits referred to in the art as computers, butbroadly refers to computers, processors, microcontrollers,microcomputers, programmable logic controllers, application specificintegrated circuits, and other programmable circuits. As used herein, anelement or step recited in the singular and proceeded with the word “a”or “an” should be understood as not excluding plural said elements orsteps, unless such exclusion is explicitly recited. Furthermore,references to “one embodiment” of the present invention are not intendedto be interpreted as excluding the existence of additional embodimentsthat also incorporate the recited features.

Also as used herein, the phrase “reconstructing an image” is notintended to exclude embodiments of the present invention in which datarepresenting an image is generated but a viewable image is not.Therefore, as used herein the term, “image,” broadly refers to bothviewable images and data representing a viewable image. However, manyembodiments generate (or are configured to generate) at least oneviewable image.

FIG. 3 is a schematic illustration of an exemplary cone beam (CB)geometry 300 that may be used with system 10 (shown in FIG. 1). FIG. 4is a schematic illustration of an exemplary cone-parallel geometry 400,which can be obtained by a row-wise fan-to-parallel rebinning in theoriginal CB geometry (shown in FIG. 3). In the exemplary embodiment, aCB reconstruction algorithm using cone-angle-and-image-plane-dependentview weighting is described using the cone-parallel geometry.

The Feldkamp, Davis, and Kress (FDK) algorithm based on thecone-parallel geometry can be expressed as: $\begin{matrix}{{{f\left( {x,y,z} \right)} = {\frac{1}{2}{\int_{0}^{2\pi}{{\left\lbrack {\mathbb{d}^{2}{/\left( {\mathbb{d}^{2}{+ Z^{2}}} \right)^{1/2}}} \right\rbrack\left\lbrack {\int_{- \infty}^{+ \infty}{{S_{\beta}\left( {\omega,Z} \right)}{\mathbb{e}}^{j\quad 2\quad\pi\quad\omega\quad x}{\omega }{\mathbb{d}\omega}}} \right\rbrack}{\mathbb{d}\beta}}}}},{and}} & (1) \\{{{S_{\beta}\left( {\omega,Z} \right)} = {\int_{- \infty}^{\infty}{{P_{\beta}\left( {t,Z} \right)}{\mathbb{e}}^{{- j}\quad 2\pi\quad\omega\quad t}{\mathbb{d}t}}}},} & (2)\end{matrix}$where, β represents the view angle;

ƒ(x,y,z) represents the point to be reconstructed;

P_(β)(t,Z) represents the projection of ƒ(x,y,z) in the virtual detectorD′;

d represents the orthogonal distance between the x-ray focal spot andthe virtual detector; and

Z represents the height of the projection of ƒ(x,y,z) in the virtualdetector.

In addition to the recognition that the generation of CB artifacts inimages reconstructed by the FDK algorithm is because the FDK algorithmdoes not satisfy the DSC, another insight into the root cause of the CBartifacts is that there exist inconsistence between conjugate rays.Conjugate rays are rays that are 180° apart in view angle.

FIG. 5 is a schematic illustration of an exemplary geometry 500 of adirect-ray and its conjugate ray. In the exemplary embodiment, ray SP isthe direct ray determined by (α,β,t), S′P is the conjugate raydetermined by (α_(c),β+π,−t), t is the orthogonal distance between O andline SS′, and l the distance between the image plane and the centralplane determined by the circular source trajectory.

Direct ray SP and its conjugate ray S′P do not pass through the samepath. This difference is called “inconsistence” and is pixel dependent.The inconsistence varies dramatically over the location of pixels to bereconstructed. Moreover, the larger the distance between an image plane(IP) in which the image is to be reconstructed and the central plane(CP) determined by the circular trajectory, the more severe theinconsistency over image pixels. As shown in equations (1)-(2), the FDKalgorithm treats all rays equally, resulting in CB artifacts that can bereduced if an appropriate view weighting strategy is exercised.

Without extra trajectories supplemental to the circular trajectory, themodified FDK algorithm described herein applies a cone-angle-dependentview weighting on projection data. The cone-angle-dependent viewweighting significantly reduces the inconsistency between conjugate raysby suppressing the contribution from one of the conjugate samples with alarger cone angle. Furthermore, the view weighting's dependence oncone-angle should increase with the distance between IP and CP, becausethe inconsistency severity of the pixels within an IP is proportional tothe distance. Inclusively, based on the cone-parallel geometryillustrated in FIG. 4, the modified FDK algorithm can be expressed as$\begin{matrix}{{{f\left( {x,y,z} \right)} = {\frac{1}{2}{\int_{0}^{2\pi}{{\left\lbrack {\mathbb{d}^{2}{/\left( {\mathbb{d}^{2}{+ Z^{2}}} \right)^{1/2}}} \right\rbrack\left\lbrack {\int_{- \infty}^{+ \infty}{{w\left( {l,\alpha} \right)}{S_{\beta}\left( {\omega,Z} \right)}{\mathbb{e}}^{j\quad 2\quad\pi\quad\omega\quad x}{\omega }{\mathbb{d}\omega}}} \right\rbrack}{\mathbb{d}\beta}}}}},{and}} & (3) \\{{S_{\beta}\left( {\omega,Z} \right)} = {\int_{- \infty}^{\infty}{{P_{\beta}\left( {t,Z} \right)}{\mathbb{e}}^{{- j}\quad 2\pi\quad\omega\quad t}{{\mathbb{d}t}.}}}} & (4)\end{matrix}$where α represents the cone angle of the ray emanating from the focalspot and passing through point P;

-   l is the orthogonal distance between IP and CP; and-   w (l,α) is the cone-angle-and-image-plane-dependent view weighting    function.

Generally, the view weighting function w(l,α) meets the followingconditions:0≦w(l,α)≦1.0  (5)w(l,α ₁)≧w(l,α ₂) while α₁≦α₂  (6)and a special case of the view weighting function w(l,α) is given belowas an example: $\begin{matrix}{{w\left( {l,\alpha} \right)} = \frac{\tan^{g{(l)}}\alpha_{c}}{{\tan^{g{(l)}}\alpha} + {\tan^{g{(l)}}\alpha_{c}}}} & (7)\end{matrix}$where g(l) is a positive monotonically increasing function over thedistance l, for example,g(l)≧0  (8)g(l ₁)≦g(l ₂) while l ₁ ≦l ₂  (9)

A mechanism underlying the modified FDK algorithm described in equations(3)-(9) is that one of the conjugate rays with smaller cone angle isgiven a favorable weight while the other with larger cone angle is givena smaller weight.

Generally, if IP is far away from the CP or close to the boundary row ofa detector, data extrapolation is needed for 3D backprojection toreconstruct the image. Given a pixel P to be reconstructed, it ispossible for one of the conjugate rays passing through pixel P to hitinside of the detector, but the other ray to hit outside of thedetector. The conjugate rays hitting inside of the detector should begiven larger weight, while the rays hitting outside of the detectorshould earn a smaller weight. This can be done by incorporating an extraterm in equations (7)˜(9) as shown below: $\begin{matrix}{{w\left( {l,\alpha,z} \right)} = \frac{\tan^{({{g{(l)}} + {f{(v_{c})}}})}\alpha_{c}}{{\tan^{({{g{(l)}} + {f{(v)}}})}\alpha} + {\tan^{({{g{(l)}} + {f{(v_{c})}}})}\alpha_{c}}}} & (10)\end{matrix}$where v and v_(c) are the vertical coordinates of the projection ofpixel P in the detector corresponding to each of the conjugate rays,respectively. ƒ(ν) and ƒ(ν_(c)) can be defined as: $\begin{matrix}{{f(v)} = \left\{ \begin{matrix}{{f^{\prime}(v)} > 0} & {{{while}\quad{v}} > D} \\{0} & {{{while}\quad{v}} \leq D}\end{matrix} \right.} & (11) \\{{f\left( v_{c} \right)} = \left\{ \begin{matrix}{{f^{\prime}\left( v_{c} \right)} > 0} & {{{while}\quad{v_{c}}} > D} \\{0} & {{{while}\quad{v_{c}}} \leq D}\end{matrix} \right.} & (12)\end{matrix}$where D is the half height of the detector.Both ƒ′(ν) and ƒ′(ν_(c)) are positive monotonous increasing functions,i.e.,ƒ′(ν₁)≦ƒ′(ν₂) while ν₁≦ν₂  (13)ƒ′(ν_(c1))≦ƒ′(ν_(c2)) while ν_(c1) ≦ν _(c2)  (14)

The mechanism underlying equations (10)-(14) is that, one of theconjugate rays inside the active area of the detector is given anenhanced favorable weight while the other with larger cone angle isgiven an enhanced unfavorable weight.

Moreover, the cone-angle-and-image-plane-dependent view weighting can beextended to implement the so-called “cross-beam correction”, in whichmore than one circular source trajectories apart in z-direction areutilized to improve the image quality of the images between the CPsdetermined by those circular trajectories.

FIG. 6 is a schematic illustration of an exemplary geometry 600 ofdirect-rays and conjugate rays associated with a dual circulartrajectories. Ray S₁P (α₁,β,t) and S′₁P (α_(1c), β+π, −t) are theconjugate rays corresponding to trajectory 1, and ray S₂P (α₂,β,t) andS′₂P (α_(2c),β+π,−t) are the conjugate rays corresponding to trajectory2. The distance between the IP and trajectory 1 is l, and the distancebetween the IP and trajectory 2 is L-l. For each trajectory, the viewweighting function is defined as: $\begin{matrix}{{{w_{1}\left( {l,\alpha,z} \right)} = {0.5\frac{\tan^{g{(l)}}\alpha_{1c}}{{\tan^{g{(l)}}\alpha_{1}} + {\tan^{g{(l)}}\alpha_{1c}}}}},} & (15) \\{{w_{2}\left( {l,\alpha,z} \right)} = {0.5{\frac{\tan^{g{({L - l})}}\alpha_{2c}}{{\tan^{g{({L - l})}}\alpha_{2}} + {\tan^{g{({L - l})}}\alpha_{2c}}}.}}} & (16)\end{matrix}$

The above-described embodiments of an imaging system facilitate reducingcone beam artifacts. Exemplary embodiments of imaging system methods andapparatus are described above in detail. The imaging system componentsillustrated are not limited to the specific embodiments describedherein, but rather, components of each imaging system may be utilizedindependently and separately from other components described herein. Forexample, the imaging system components described above may also be usedin combination with different imaging systems. A technical effect of thevarious embodiments of the systems and methods described herein includeat least one of facilitating imaging a patient with images wherein thecone beam artifacts have been substantially reduced.

While the invention has been described in terms of various specificembodiments, those skilled in the art will recognize that the inventioncan be practiced with modification within the spirit and scope of theclaims.

1. A computer programmed to generate computed tomographic (CT) imagesfrom a set of projection data acquired during a CT scan, said computerprogrammed to perform at least one of a cone angle dependent viewweighting and an image plane dependent view weighting.
 2. A computer inaccordance with claim 1 further programmed to apply a Feldkamp, Davis,and Kress (FDK) algorithm with at least one of a cone angle dependentview weighting and an image plane dependent view weighting to the set ofprojection data.
 3. A computer in accordance with claim 2 furtherprogrammed to apply an FDK algorithm to a single circular sourcetrajectory expressed as: $\begin{matrix}{{{{f\left( {x,y,z} \right)} = {\frac{1}{2}{\int_{0}^{2\pi}{{\left\lbrack {\mathbb{d}^{2}{/\left( {\mathbb{d}^{2}{+ Z^{2}}} \right)^{1/2}}} \right\rbrack\left\lbrack {\int_{- \infty}^{+ \infty}{{w\left( {l,\alpha} \right)}{S_{\beta}\left( {\omega,Z} \right)}{\mathbb{e}}^{j\quad 2\quad\pi\quad\omega\quad x}{\omega }{\mathbb{d}\omega}}} \right\rbrack}{\mathbb{d}\beta}}}}};}{and}} \\{{{S_{\beta}\left( {\omega,Z} \right)} = {\int_{- \infty}^{\infty}{{P_{\beta}\left( {t,Z} \right)}{\mathbb{e}}^{{- j}\quad 2\pi\quad\omega\quad t}{\mathbb{d}t}}}},}\end{matrix}$ where β represents view angle; ƒ(x,y,z) represents thepoint to be reconstructed; P₆₂(t, Z) represents the projection ofƒ(x,y,z) in the virtual detector D′; d represents the orthogonaldistance between the x-ray focal spot and the virtual detector; Zrepresents the height of the projection of ƒ(x,y,z) in the virtualdetector; w(l,α) represents a cone-angle-and-image-plane-dependent viewweighting function; α represents the cone angle of the ray emanatingfrom the focal spot and passing through a point P; and l represents anorthogonal distance between an imaging plane (IP) and a central plane(CP).
 4. A computer in accordance with claim 3 whereincone-angle-and-image-plane-dependent view weighting function w(l,α)meets conditions:0≦w(l,α)≦1.0 andw(l,α ₁)≦w(l,α ₂) while α₁≦α₂.
 5. A computer in accordance with claim 3wherein conjugate rays are rays that are 180° apart in view angle, saidcomputer further programmed to weight a first ray associated with arelatively larger cone angle less than a second ray associated with arelatively smaller cone angle, the rays being conjugates with respect toeach other.
 6. A computer in accordance with claim 3 wherein one of aray passing through a pixel P and a conjugate of the ray impinge on thedetector, said computer further programmed to weight the ray impingingthe detector relatively greater than the ray not impinging the detectorwhen reconstructing pixel P.
 7. A computer in accordance with claim 3wherein the cone-angle-and-image-plane-dependent view weighting functionis expressed as:${w\left( {l,\alpha} \right)} = \frac{\tan^{g{(l)}}\alpha_{c}}{{\tan^{g{(l)}}\alpha} + {\tan^{g{(l)}}\alpha_{c}}}$where g(l) is a positive monotonically increasing function over distancel.
 8. A computer in accordance with claim 7 wherein g(l) meets thefollowing conditions:g(l)≧2 , andg(l)≦g(l ₂) while l ₁ ≦l ₂.
 9. A computer in accordance with claim 3wherein the cone-angle-and-image-plane-dependent view weighting functionis expressed as:${{w\left( {l,\alpha,z} \right)} = \frac{\tan^{({{g{(l)}} + {f{(v_{c})}}})}\alpha_{c}}{{\tan^{({{g{(l)}} + {f{(v)}}})}\alpha} + {\tan^{({{g{(l)}} + {f{(v_{c})}}})}\alpha_{c}}}},$where ν and ν_(c) are the vertical coordinates of the projection ofpixel P in the detector corresponding to each of the conjugate rays,respectively.
 10. A computer in accordance with claim 9 wherein ƒ(ν) andƒ(ν_(c)) are defined as: $\begin{matrix}{{f(v)} = \left\{ {\begin{matrix}{{f^{\prime}(v)} > 0} & {{{while}\quad{v}} > D} \\{0} & {{{while}\quad{v}} \leq D}\end{matrix},{and}} \right.} \\{{f\left( v_{c} \right)} = \left\{ {\begin{matrix}{{f^{\prime}\left( v_{c} \right)} > 0} & {{{while}\quad{v_{c}}} > D} \\{0} & {{{while}\quad{v_{c}}} \leq D}\end{matrix}.} \right.}\end{matrix}$
 11. A computer in accordance with claim 10 wherein ƒ′(ν)and ƒ′(ν_(c)) are positive monotonous increasing functions.
 12. Acomputer in accordance with claim 11 wherein ƒ′(ν) and ƒ′(νhd c) meetthe conditions:ƒ′(ν₁)≦ƒ′(ν₂) while ν₁≦ν₂, andƒ′(ν_(cl))≦ƒ′(ν_(c2)) while ν_(c1)≦ν_(c2).
 13. A computer in accordancewith claim 3 wherein more than one circular source trajectories spacedapart in the z-direction define respective central planes such that adistance between the image plane and a first trajectory is l, and adistance between the IP and a second trajectory is L-l and wherein foreach trajectory, the cone-angle-and-image-plane-dependent view weightingfunction is expressed as:${{w_{1}\left( {l,\alpha,z} \right)} = {0.5\frac{\tan^{g{(l)}}\alpha_{1c}}{{\tan^{g{(l)}}\alpha_{1}} + {\tan^{g{(l)}}\alpha_{1c}}}}},{{w_{2}\left( {l,\alpha,z} \right)} = {0.5{\frac{\tan^{g{({L - l})}}\alpha_{2c}}{{\tan^{g{({L - l})}}\alpha_{2}} + {\tan^{g{({L - l})}}\alpha_{2c}}}.}}}$14. A method for producing a cross-sectional image of an object by usinga computed tomography imaging system, which includes a source of aconical beam of radiation and a multi-row detector array arranged onopposite sides of an axis of rotation, said method comprising: rotatingthe source and detector array about the axis of rotation; whilerotating, collecting x-ray attenuation data samples from the multi-rowdetector array at a plurality of projection angles to produce a set ofprojection data measured with a circular orbit of the x-ray source; andgenerating an image from the set of projection data using at least oneof a cone angle dependent view weighting and an image plane dependentview weighting.
 15. A method in accordance with claim 14 wherein aFeldkamp, Davis, and Kress (FDK) algorithm is utilized in generating theimage.
 16. A method in accordance with claim 15 wherein the FDKalgorithm utilizes a cone angle dependent view weighting in generatingthe image.
 17. A method in accordance with claim 15 wherein the FDKalgorithm utilizes an FDK algorithm applied to a single circular sourcetrajectory expressed as:${{f\left( {x,y,z} \right)} = {\frac{1}{2}{\int_{0}^{2\pi}{{\left\lbrack {\mathbb{d}^{2}{/\left( {\mathbb{d}^{2}{+ Z^{2}}} \right)^{1/2}}} \right\rbrack\left\lbrack {\int_{- \infty}^{+ \infty}{{w\left( {l,\alpha} \right)}{S_{\beta}\left( {\omega,Z} \right)}{\mathbb{e}}^{{j2\pi\omega}\quad x}{\omega }{\mathbb{d}\omega}}} \right\rbrack}{\mathbb{d}\beta}}}}};$and S_(β)(ω, Z) = ∫_(−∞)^(∞)P_(β)(t, Z)𝕖^(−j2πω  t)𝕕t where β representsview angle; ƒ(x,y,z) represents the point to be reconstructed;P_(β)(t,Z) represents the projection of ƒ(x,y,z) in the virtual detectorD′; d represents the orthogonal distance between the x-ray focal spotand the virtual detector; Z represents the height of the projection ofƒ(x,y,z) in the virtual detector; w(l,α) represents acone-angle-and-image-plane-dependent view weighting function; αrepresents the cone angle of the ray emanating from the focal spot andpassing through a point P; and l represents an orthogonal distancebetween an imaging plane (IP) and a central plane (CP).
 18. A method inaccordance with claim 17 wherein cone-angle-and-image-plane-dependentview weighting function w(l,α) meets conditions:0≦w(l,α)≦1.0 andw(l,α ₁)≦w(l,α ₂) while α₁≦α₂.
 19. A method in accordance with claim 17wherein conjugate rays are rays that are 180° apart in view angle, saidmethod further comprising weighting a first ray associated with arelatively larger cone angle less than a second ray associated with arelatively smaller cone angle, the rays being conjugates with respect toeach other.
 20. A method in accordance with claim 17 wherein one of aray passing through a pixel P and a conjugate of the ray impinge on thedetector, said method further comprising weighting the ray impinging thedetector relatively greater than the ray not impinging the detector whenreconstructing pixel P.
 21. A method in accordance with claim 17 whereinthe cone-angle-and-image-plane-dependent view weighting function isexpressed as:${w\left( {l,\alpha} \right)} = \frac{\tan^{g{(l)}}\alpha_{c}}{{\tan^{g{(l)}}\alpha} + {\tan^{g{(l)}}\alpha_{c}}}$where g(l) is a positive monotonically increasing function over distancel.
 22. A method in accordance with claim 21 wherein g(l) meets thefollowing conditions:g(l)≧0, andg(l ₁)≦g(l ₂) while l ₁ ≦l ₂.
 23. A method in accordance with claim 17wherein the cone-angle-and-image-plane-dependent view weighting functionis expressed as:${{w\left( {l,\alpha,z} \right)} = \frac{\tan^{({{g{(l)}} + {f{(v_{c})}}})}\alpha_{c}}{{\tan^{({{g{(l)}} + {f{(v)}}})}\alpha} + {\tan^{({{g{(l)}} + {f{(v_{c})}}})}\alpha_{c}}}},$where ν and ν_(c) are the vertical coordinates of the projection ofpixel P in the detector corresponding to each of the conjugate rays,respectively.
 24. A method in accordance with claim 23 wherein ƒ(ν) andƒ(ν_(c)) are defined as: ${f(v)} = \left\{ {\begin{matrix}{{f^{\prime}(v)} > 0} & {while} & {{v} > D} \\0 & {while} & {{v} \leq D}\end{matrix},\quad{{{and}{f\left( v_{c} \right)}} = \left\{ {\begin{matrix}{{f^{\prime}\left( v_{c} \right)} > 0} & {while} & {{v_{c}} > D} \\0 & {while} & {{v_{c}} \leq D}\end{matrix}.} \right.}} \right.$
 25. A method in accordance with claim24 wherein ƒ′(v) and ƒ′(v_(c)) are positive monotonous increasingfunctions.
 26. A method in accordance with claim 25 wherein ƒ′(v) andƒ′(v_(c)) meet the conditions:ƒ′(v ₁)≦ƒ′(ν₂) while ν₁≦ν₂, andƒ′(ν_(cl))≦ƒ′(ν_(c2)) while ν_(c1)≦ν_(c2).
 27. A method in accordancewith claim 17 wherein more than one circular source trajectories spacedapart in the z-direction define respective central planes such that adistance between the image plane and a first trajectory is l, and adistance between the IP and a second trajectory is L-l and wherein foreach trajectory, the cone-angle-and-image-plane-dependent view weightingfunction is expressed as:${{w_{1}\left( {l,\alpha,z} \right)} = {0.5\frac{\tan^{g{(l)}}\alpha_{1c}}{{\tan^{g{(l)}}\alpha_{1}} + {\tan^{g{(l)}}\alpha_{1c}}}}},{{w_{2}\left( {l,\alpha,z} \right)} = {0.5{\frac{\tan^{g{({L - l})}}\alpha_{2c}}{{\tan^{g{({L - l})}}\alpha_{2}} + {\tan^{g{({L - l})}}\alpha_{2c}}}.}}}$28. A computed tomographic (CT) imaging system for reconstructing animage of an object, said imaging system comprising: a detector array; atleast one radiation source; and a computer coupled to said detectorarray and said radiation source, said computer configured to utilize acone-angle-and-image-plane-dependent view weighting function to generatethree dimensional images from cone-beam projections measured with acircular orbit of the radiation source.
 29. An imaging system inaccordance with claim 28 wherein said computer is further configured toapply a cone-angle-and-image-plane-dependent view weighting function toa Feldkamp, Davis, and Kress (FDK) algorithm.
 30. An imaging system inaccordance with claim 28 wherein said computer is further configured toapply a cone-angle-and-image-plane-dependent view weighting function tothe FDK algorithm expressed as:${{f\left( {x,y,z} \right)} = {\frac{1}{2}{\int_{0}^{2\pi}{{\left\lbrack {\mathbb{d}^{2}{/\left( {\mathbb{d}^{2}{+ Z^{2}}} \right)^{1/2}}} \right\rbrack\left\lbrack {\int_{- \infty}^{+ \infty}{{w\left( {l,\alpha} \right)}{S_{\beta}\left( {\omega,Z} \right)}{\mathbb{e}}^{{j2\pi\omega}\quad x}{\omega }{\mathbb{d}\omega}}} \right\rbrack}{\mathbb{d}\beta}}}}};$and S_(β)(ω, Z) = ∫_(−∞)^(∞)P_(β)(t, Z)𝕖^(−j2πω  t)𝕕t where p representsview angle; ƒ(x,y,z) represents the point to be reconstructed;P_(β)(t,Z) represents the projection of ƒ(x,y,z) in the virtual detectorD′; d represents the orthogonal distance between the x-ray focal spotand the virtual detector; Z represents the height of the projection ofƒ(x,y,z) in the virtual detector; w(l,α) represents acone-angle-and-image-plane-dependent view weighting function; αrepresents the cone angle of the ray emanating from the focal spot andpassing through a point P; and l represents an orthogonal distancebetween an imaging plane (IP) and a central plane (CP).
 31. A computerin accordance with claim 30 wherein cone-angle-and-image-plane-dependentview weighting function w(l,α) meets conditions:0≦w(l,α)≦1.0 andw(l,α ₁)≦w(l,α ₂) while α₁≦α₂.
 32. An imaging system in accordance withclaim 30 wherein conjugate rays are rays that are 180° apart in viewangle, said computer further configured to weight a first ray associatedwith a relatively larger cone angle less than a second ray associatedwith a relatively smaller cone angle, the rays being conjugates withrespect to each other.
 33. An imaging system in accordance with claim 30wherein one of a ray passing through a pixel P and a conjugate of theray impinge on the detector, said computer further configured to weightthe ray impinging the detector relatively greater than the ray notimpinging the detector when reconstructing pixel P.
 34. An imagingsystem in accordance with claim 30 wherein thecone-angle-and-image-plane-dependent view weighting function isexpressed as:${w\left( {l,\alpha} \right)} = \frac{\tan^{g{(l)}}\alpha_{c}}{{\tan^{g{(l)}}\alpha} + {\tan^{g{(l)}}\alpha_{c}}}$where g(l) is a positive monotonically increasing function over distancel.
 35. An imaging system in accordance with claim 34 wherein g(l) meetsthe following conditions:g(l)≧2, andg(l ₁)≦g(l ₂) while l ₁ ≦l ₂.
 36. An imaging system in accordance withclaim 30 wherein the cone-angle-and-image-plane-dependent view weightingfunction is expressed as:${{w\left( {l,\alpha,z} \right)} = \frac{\tan^{({{g{(l)}} + {f{(v_{c})}}})}\alpha_{c}}{{\tan^{({{g{(l)}} + {f{(v)}}})}\alpha} + {\tan^{({{g{(l)}} + {f{(v_{c})}}})}\alpha_{c}}}},$where ν and ν_(c) are the vertical coordinates of the projection ofpixel P in the detector corresponding to each of the conjugate rays,respectively.
 37. An imaging system in accordance with claim 36 whereinf(v) and ƒ(ν_(c)) are defined as: ${f(v)} = \left\{ {\begin{matrix}{{f^{\prime}(v)} > 0} & {while} & {{v} > D} \\0 & {while} & {{v} \leq D}\end{matrix},\quad{{{and}{f\left( v_{c} \right)}} = \left\{ {\begin{matrix}{{f^{\prime}\left( v_{c} \right)} > 0} & {while} & {{v_{c}} > D} \\0 & {while} & {{v_{c}} \leq D}\end{matrix}.} \right.}} \right.$
 38. An imaging system in accordancewith claim 37 wherein ƒ′(v) and ƒ′(v_(c)) are positive monotonousincreasing functions.
 39. An imaging system in accordance with claim 38wherein ƒ′(v) and ƒ′(v_(c)) meet the conditions:ƒ′(ν₁)≦ƒ′(ν₂) while ν₁≦ν₂ andƒ′(ν_(c1))≦ƒ′(ν_(c2)) while ν_(c1)≦ν_(c2).
 40. An imaging system inaccordance with claim 30 wherein more than one circular sourcetrajectories spaced apart in the z-direction define respective centralplanes such that a distance between the image plane and a firsttrajectory is l, and a distance between the IP and a second trajectoryis L-l and wherein for each trajectory the imaging system is furtherconfigured to express the cone-angle-and-image-plane-dependent viewweighting function as:${{w_{1}\left( {l,\alpha,z} \right)} = {0.5\frac{\tan^{g{(l)}}\alpha_{1c}}{{\tan^{g{(l)}}\alpha_{1}} + {\tan^{g{(l)}}\alpha_{1c}}}}},{{w_{2}\left( {l,\alpha,z} \right)} = {0.5{\frac{\tan^{g{({L - l})}}\alpha_{2c}}{{\tan^{g{({L - l})}}\alpha_{2}} + {\tan^{g{({L - l})}}\alpha_{2c}}}.}}}$